CN112232714B - Deep learning-based risk assessment method for distribution network under incomplete structural parameters - Google Patents

Deep learning-based risk assessment method for distribution network under incomplete structural parameters Download PDF

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CN112232714B
CN112232714B CN202011296072.7A CN202011296072A CN112232714B CN 112232714 B CN112232714 B CN 112232714B CN 202011296072 A CN202011296072 A CN 202011296072A CN 112232714 B CN112232714 B CN 112232714B
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肖浩
裴玮
杨艳红
马腾飞
孔力
王新迎
张国宾
王天昊
马世乾
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State Grid Corp of China SGCC
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China Electric Power Research Institute Co Ltd CEPRI
State Grid Tianjin Electric Power Co Ltd
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Abstract

A risk assessment method for a distribution network under incomplete structural parameters based on deep learning comprises the following steps: 1) Counting the external available historical operation data of an incomplete area of the structural parameter information in the power distribution network, and establishing an equivalent packaging model by deep learning training; 2) Substituting the regional weather data and the electricity price data of the region predicted in the day before into an equivalent model to predict probability distribution of gateway interaction power between the region with incomplete structural parameter information and the power distribution network; 3) Constructing equivalent estimation points and calculating probability power flow of the power distribution network; 4) And (5) counting probability distribution of state variables in the power distribution network, and completing overall operation risk assessment of the power distribution network. The method can realize the running risk assessment of the power distribution network under the condition of incomplete structural parameters, avoids the problems that the traditional analysis method and the random sampling method need complete information to carry out probability power flow calculation and risk assessment, and is beneficial to improving the access level of distributed renewable energy sources of the power distribution network and improving the running safety and reliability of the power distribution network.

Description

Deep learning-based risk assessment method for distribution network under incomplete structural parameters
Technical Field
The invention relates to a risk assessment method for a distribution network under incomplete structural parameters.
Background
In recent years, distributed power sources such as distributed photovoltaic and wind power are rapidly developed, and the access permeability of the power distribution network is gradually increased year by year. The risk of operation of the distribution network is also greatly increased due to the strong randomness and uncertainty of distributed photovoltaics and wind power. Meanwhile, due to the relative lag of informatization construction of the distribution network, particularly a rural distribution network, a large amount of 'blind areas' for information acquisition still exist, so that the distribution network is difficult to acquire complete system structure parameter information in risk assessment, and serious challenges are brought to risk management and control and safe and stable operation of the regional distribution network, so that how to reasonably and effectively assess the operation risk of the distribution network under the conditions that a large amount of random distributed power supplies are accessed and network structure parameters are not clear becomes a critical problem to be solved by a regional power grid regulation center.
At present, aiming at the evaluation of the running risk of the power distribution network, the main analysis and evaluation methods comprise an analysis method and a random sampling method. The first type of analysis method is mainly used for obtaining semi-invariant or estimated points of the fluctuation quantity of the input power of each node by analyzing probability density functions of distributed energy and load random variables, substituting the semi-invariant or estimated points into deterministic power flow calculation to obtain semi-invariant or estimated points of state variables such as voltage amplitude, phase angle and the like of an output node, and finally fitting probability distribution of the state variables and evaluating operation risk of a system according to a series expansion method. The second random sampling rule is to generate a large number of samples describing uncertainty of distributed energy and load output through random sampling, then to calculate a large number of power flows according to the samples, and finally to fit the statistical power flow results to the probability distribution of the state variables such as voltage amplitude, phase angle and the like of the output node. However, in either of the above modes, all network structure parameter information needs to be learned, and then complete power flow calculation can be performed to obtain state variables such as voltage amplitude and phase angle of an output node, so that the risk assessment analysis of the power distribution network under the condition of incomplete structure parameter information is difficult to continue to be applicable.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a power distribution network risk assessment method based on deep learning, realizes power distribution network operation risk modeling under incomplete structural parameters, solves the problems that the traditional analysis method and the random sampling method need complete information to carry out probability trend calculation and risk assessment, lays a foundation for the formulation of a power distribution network risk management and control strategy, is beneficial to improving the operation reliability of the power distribution network, improves the access level of distributed renewable energy sources, and has important theoretical and practical significance for reasonable and orderly development of distributed energy sources and the power distribution network.
The invention discloses a risk assessment method for a distribution network under incomplete structural parameters based on deep learning, which comprises the following steps:
(1) The outside of the incomplete area of the statistical structural parameter information can acquire historical operation data, such as local historical wind speed, illumination, electricity price, temperature and gateway interaction power between the area and the power distribution network, and an equivalent model of the incomplete area of the structural parameter information is trained and established;
(2) Predicting probability distribution of meteorological data such as wind speed, illumination, temperature and the like and electricity price data before the day, substituting the probability distribution into an equivalent model of an area with incomplete structural parameter information, and calculating probability distribution of gateway interaction power between the area and a power distribution network;
(3) Constructing equivalent estimation points according to the predicted gateway interaction power probability distribution between the incomplete structure parameter information area and the power distribution network, and carrying out power distribution network probability load flow calculation;
(4) And (3) counting probability power flow calculation results of the power distribution network, analyzing probability distribution of state variables such as voltage amplitude, phase angle and the like of each node in the power distribution network, and evaluating overall operation risk of the power distribution network.
In the step (1), historical operation data including local historical wind speed, illumination, electricity price, temperature and gateway interaction power between the area and a power distribution network can be acquired outside the area with incomplete structural parameter information, and an equivalent model of the area with incomplete structural parameter information is built through training; the method specifically comprises the steps of data preprocessing, regional equivalent model packaging training, test verification and updating of a training model and the like:
step (1-1): the outside of the incomplete area of statistical analysis structural parameter information can acquire historical operation data, such as local historical illumination, wind speed, temperature, electricity price and gateway interaction power between the area and a power distribution network, and the data per unit, training set and test set division and other preprocessing is carried out on the historical operation data, as shown in formula (1):
Figure GDA0004231453980000021
in the formula ,Ds Historical data set representing illumination, wind speed, temperature, electricity price and gateway interaction power between incomplete structural parameter information area and power distribution network, wherein M is total number of days of historical data, and L k 、W k 、T k 、E k 、P g,k Respectively representing illumination, wind speed, temperature, electricity price and structural parameter information incomplete area on the kth day and a gateway interaction power data set between the distribution network,
Figure GDA0004231453980000031
respectively representing illumination, wind speed, temperature, electricity price, and gate interaction power between the incomplete structural parameter information area and the power distribution network at the kth and the d time period, wherein N represents the total time period number of a daily data set,'>
Figure GDA0004231453980000032
Representing the data set after per unit of the historical data set, min (·) representing the minimum value, and max (·) representing the maximum value,/->
Figure GDA0004231453980000033
Representing the training set taken from the per unit data set,/for>
Figure GDA0004231453980000034
Represents the test set taken from the per-unit data set and epsilon represents the proportion of the training set.
Step (1-2): learning and training the training set data by adopting a long-short-term memory neural network (LSTM), and establishing an equivalent encapsulation model of the incomplete area of the structural parameter information, wherein the equivalent encapsulation model is shown in a formula (2):
Figure GDA0004231453980000035
in the formula ,xt Represents the t-th step of the current iteration from the training dataset
Figure GDA0004231453980000036
Taken out of the middleData sets of illumination, wind speed, temperature and electricity price; h is a t-1 Representing +.>
Figure GDA0004231453980000037
The gateway interaction power set between the incomplete area of the extracted structural parameter information and the power distribution network is accumulated; f (f) t Representing forget gate output, w corresponding to the t step of the current iteration f and bf For the weight coefficient and bias coefficient of each neuron in the forgetting layer, sigma (·) represents an s-type curve function, i t Representing the output of the t-th input layer of the current iteration, w i and bi For weighting and bias coefficients of the neurons in the input layer, < >>
Figure GDA0004231453980000038
Representing estimated output of the convolution layer of the t step of the current iteration, w c and bc For the weighting and bias coefficients of each neuron in the convolution layer, tanh (·) represents the hyperbolic tangent function, c t Representative of the actual output of the current iteration step t convolution layer, o t Represents the output of the t-th output layer of the current iteration, w o and bo For the weight coefficient and bias coefficient of each neuron in the output layer, h t Representing the gateway interaction power between the incomplete structural parameter information area obtained by actual prediction of the t step of the current iteration and the power distribution network.
Step (1-3): substituting the test set data to test and verify the equivalent packaging model, and optimally calculating and updating the weight coefficient and the bias coefficient of each layer of neurons of a long-short-time memory neural network (LSTM) according to the feedback result until the root mean square error converges:
1) Substituting test set data into an equivalent packaging model, and calculating a predicted value of the gateway interaction power between the incomplete area of the structural parameter information and the power distribution network:
Figure GDA0004231453980000039
in the formula ,
Figure GDA0004231453980000041
representing a predicted value of gate interaction power between the incomplete area of the structural parameter information and the power distribution network; x is x test Representing +.>
Figure GDA0004231453980000042
The data set of the illumination, wind speed, temperature and electricity price taken out from the device; f (F) grid (. Cndot.) refers to the equivalent encapsulation model of the incomplete area of the parameter information calculated in the step (1-2).
2) Comparing the predicted value and the actual value of the gate interaction power between the incomplete structure parameter information area and the power distribution network, and calculating the predicted root mean square error of the current packaging model, wherein the predicted root mean square error is shown in the following formula:
Figure GDA0004231453980000043
wherein, RMSE represents the prediction root mean square error of the current training encapsulation equivalent model; m is the number of the predicted total time period, t is the time period number,
Figure GDA0004231453980000044
representing +.>
Figure GDA0004231453980000045
The actual sampling value of the gate interaction power between the incomplete area of the structural parameter information taken out in the process and the power distribution network is +.>
Figure GDA0004231453980000046
Representing the predicted value of the gate interaction power between the incomplete area of the structural parameter information predicted by the formula (3) and the power distribution network.
3) And taking the statistical prediction root mean square error of the current encapsulation model as a target, taking the weight coefficient of each layer of neurons of the long short time memory neural network (LSTM) as an optimization decision variable, adopting a particle swarm algorithm to perform optimization calculation and adjusting the weight coefficient and the bias coefficient of each layer of neurons of the long short time memory neural network (LSTM) until the target converges. The following formula is shown:
Figure GDA0004231453980000047
Wherein, RMSE refers to root mean square error of power prediction by adopting an equivalent encapsulation model;
Figure GDA0004231453980000048
respectively taking the minimum and maximum values of the weight coefficients of the convolution layer; />
Figure GDA0004231453980000049
Respectively the minimum maximum value of the bias coefficients of the convolution layers;
Figure GDA00042314539800000410
Figure GDA00042314539800000411
respectively taking the minimum and maximum values of the weight coefficients of the input layer; />
Figure GDA00042314539800000412
Respectively taking the minimum and maximum values of the bias coefficients of the input layers; />
Figure GDA00042314539800000413
Respectively taking the minimum and maximum values of the weight coefficients of the forgetting layer; />
Figure GDA00042314539800000414
Respectively minimum and maximum values of the bias coefficients of the forgetting layers; />
Figure GDA00042314539800000415
Respectively taking the minimum and maximum values of the weight coefficients of the output layer;
Figure GDA00042314539800000416
respectively the minimum and maximum values of the bias coefficients of the output layers。
In the step (2), predicting probability distribution of weather data such as sunlight, wind speed, temperature and the like and electricity price data before the day, substituting the probability distribution into an equivalent model of a region with incomplete structural parameter information, and calculating probability distribution of gate interaction power between the region and a power distribution network, wherein the method mainly comprises the steps of sampling data samples according to the weather data such as sunlight, wind speed, temperature and the like predicted before the day and the probability distribution of the electricity price data, performing simulation calculation of the gate interaction power between the region with incomplete structural parameter information and the power distribution network, performing statistics of the probability distribution of the gate interaction power between the region with incomplete structural parameter information and the power distribution network and the like:
Step (2-1): according to the probability distribution of weather data such as illumination, wind speed, temperature and the like and electricity price data predicted in the future, latin square sampling is adopted to generate a large number of simulation data samples, as shown in a formula (6):
Figure GDA0004231453980000051
wherein ,xpv 、x wind 、x TP 、x price Respectively representing the light, wind speed, temperature and electricity price data samples obtained by sampling the kth Latin square,
Figure GDA0004231453980000052
the probability distribution functions of illumination, wind speed, temperature and electricity price data predicted in the day before are respectively shown, N is the total sample rule number sampled by Latin square, and r n Representing random numbers between 0 and 1 subject to uniform distribution, k is the order number of the latin square samples.
Step (2-2): and (3) calling an equivalent model of the structural parameter information incomplete area obtained in the step (1), and simulating, calculating and predicting the gateway interaction power between the area and the power distribution network:
Figure GDA0004231453980000053
wherein ,xpv 、x wind 、x TP 、x price Respectively representing the light, wind speed, temperature and electricity price data samples obtained by sampling Latin square at the kth time, F grid (. Cndot.) refers to the equivalent encapsulation model of the incomplete area of the parameter information calculated in the step (1-2), x pre The data set is composed of illumination, wind speed, temperature and electricity price data samples obtained by sampling the kth Latin square;
Figure GDA0004231453980000054
representing a data set formed by the gateway interaction power between the structural parameter information incomplete area obtained by simulation calculation and the power distribution network.
Step (2-3): and (3) counting a gate interaction power data set between the predicted incomplete structure parameter information area and the power distribution network, and fitting probability distribution of the gate interaction power data set:
Figure GDA0004231453980000061
wherein ,
Figure GDA0004231453980000062
the 1 st, the 2 nd, the j th and the N th components in the gateway interaction power data set between the incomplete area of the predicted structural parameter information and the power distribution network are represented respectively; n is the dimension of a gateway interaction power data set between the predicted incomplete structure parameter information area and the power distribution network; mu, sigma and lambda are respectively the mean value, variance and skewness of the gateway interaction power data set between the predicted incomplete structure parameter information area and the power distribution network, E [. Cndot.]To find the desired operator.
In the step (3), according to the predicted gateway interaction power probability distribution between the incomplete structure parameter information area and the power distribution network, constructing equivalent estimated points, and carrying out power distribution network probability load flow calculation. The method specifically comprises the steps of constructing equivalent estimated points, calculating the probability power flow of the power distribution network by point estimation and the like:
step (3-1): according to the statistical information of the gateway interaction power probability distribution between the structural parameter information incomplete area obtained by prediction in the step (2) and the power distribution network, constructing an equivalent estimation point, as shown in a formula (9):
z k ＝μ+ξ k σ k＝1,2 (9)
wherein ,zk The method comprises the steps that k estimation points corresponding to a gateway interaction power data set between a structure parameter information incomplete area and a power distribution network are adopted, wherein the value of k is 1 or 2; zeta type toy k For a kth position measurement coefficient corresponding to a gateway interaction power data set between the structure parameter information incomplete area and the power distribution network, calculating the skewness lambda of the gateway interaction power data set between the structure parameter information incomplete area and the power distribution network through a formula (10):
Figure GDA0004231453980000063
wherein ,ξk K represents the number of the estimated point and takes 1 or 2 as the k-th position measurement coefficient corresponding to the gateway interaction power data set between the incomplete area of the structural parameter information and the power distribution network; lambda is the skewness of the gateway interaction power data set between the incomplete area of the structural parameter information and the power distribution network.
Step (3-2): and taking the equivalent estimated points of the gateway interaction power data set between the constructed structure parameter information incomplete area and the power distribution network as input to calculate the power flow of the power distribution network.
1) For equivalent estimated points of the gateway interaction power data set between the constructed structure parameter information incomplete area and the power distribution network, calculating weight coefficients of the estimated points in power flow calculation of the power distribution network through a formula (11):
Figure GDA0004231453980000071
wherein ,θk For the weight coefficient occupied by the kth estimated point corresponding to the gateway interaction power data set between the incomplete area of the structural parameter information and the power distribution network in the power flow calculation, pi is a calculated intermediate variable,and the skewness lambda of the gateway interaction power data set between the incomplete structure parameter information area and the power distribution network is calculated, and k represents the number of the estimated point.
2) Estimating point z corresponding to gateway interaction power data set between imported structure parameter information incomplete area and power distribution network k Carrying out power flow calculation of the power distribution network; as shown in formula (12):
P j (k)＝f(z 1,k ,…,z i,k ,…,z M,k ,…,z M+1,k ,…,z 2M,k )k＝1,2 (12)
wherein ,Pj (k) The value of a j-th output state variable when the k-th estimated point of the power distribution network is input is obtained; f (·) is a power flow calculation equation of the power distribution network; m is the number of incomplete areas of the structural parameter information, and k represents the number of estimated points.
In the step (4), the probability flow calculation result of the power distribution network is counted, probability distribution of output state variables such as voltage amplitude, phase angle and the like of each node in the power distribution network is analyzed, and the overall operation risk of the power distribution network is estimated. The method specifically comprises the steps of statistics of moment probability distribution information of each step of each output state variable, calculation of limit crossing severity of each output state variable, evaluation of overall operation risk of the power distribution network and the like:
Step (4-1): according to the power distribution network probability power flow calculation result in the step (3), the probability distribution information of each moment of each output state variable such as the voltage amplitude, the phase angle and the like of each node of the power distribution network is statistically analyzed, and the probability distribution information is shown in a formula (13):
Figure GDA0004231453980000072
wherein ,Pj (k) And the value of the j-th output state variable when the k-th estimated point of the power distribution network is input is obtained. [ P ] j (k)] p Representative pair P j (k) To get the power of p, θ k The method comprises the steps that a weight coefficient occupied by a kth estimated point corresponding to a gateway interaction power data set between a structure parameter information incomplete area and a power distribution network in trend calculation is used, and M is the number of the structure parameter information incomplete areas;
Figure GDA0004231453980000073
substitution of j-th output state variable P in power grid j P-th order of (2), P is 1E (P j ) Represents the j-th output state variable P j Is 2 +.>
Figure GDA0004231453980000074
Represents the j-th output state variable P j Second moment of>
Figure GDA0004231453980000075
For the j-th output state variable P in the distribution network j Is a variance of (c).
Step (4-2): calculating out-of-limit values and out-of-limit severity of output state variables such as voltage of each node and branch current in a power distribution network, wherein the out-of-limit values and the out-of-limit severity are shown in the following formula:
Figure GDA0004231453980000081
Figure GDA0004231453980000082
Figure GDA0004231453980000083
wherein i is the number of a node in the power distribution network, and j is the number of a branch in the power distribution network; v (V) out,i The more limited the voltage at node I is, I out,j U is the current of branch j is the more limited value i 、U i,min 、U i,max The actual voltage value, the minimum allowable voltage amplitude and the maximum allowable voltage amplitude of the node i are respectively; i j For the actual operating current, I, of branch j j,max Maximum allowable current amplitude for branch j; s is S ev (V out,i ) For the voltage out-of-limit severity of the ith node, S ev (I out,j ) For the current out-of-limit severity of the jth branch, A i 、B i 、C i Fitting parameters, alpha, of voltage out-of-limit severity functions of ith node respectively j 、β j 、δ j Fitting parameters for the current Out-of-limit severity function of the jth branch, exp (·) represents an exponential function based on a natural constant e, and Out represents the Out-of-limit value of the voltage or current.
Step (4-3): calculating and evaluating the overall operation risk of the power distribution network according to the threshold value, the threshold severity and the threshold probability of output state variables such as voltage of each node and branch current in the power distribution network, wherein the overall operation risk is shown in the following formula:
Figure GDA0004231453980000084
wherein R is a total running risk value of the system, i is the number of nodes in the power distribution network, D is the total number of nodes in the power distribution network, j is the number of branches in the power distribution network, and L is the total number of branches in the power distribution network;
Figure GDA0004231453980000085
for the voltage cumulative distribution function of node i, +.>
Figure GDA0004231453980000086
For the current cumulative distribution function of branch j, S ev (V out,i ) For the voltage out-of-limit severity of node i, S ev (I out,j ) The current out-of-limit severity for branch j.
Figure GDA0004231453980000087
The probability density function of the corresponding node voltage can be calculated according to the probability distribution information of the voltage state variables of each node in the formula (13), and then the probability density function is obtained by integrating and solving. / >
Figure GDA0004231453980000088
The probability density function of the corresponding branch current can be calculated according to the probability distribution information of the state variables of the branch current in the formula (13), and then the probability density function is integrated and solved.
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Fig. 1 is a flow chart of risk assessment of a distribution network under incomplete structural parameters based on deep learning.
Detailed Description
The invention discloses a risk assessment method for a distribution network under incomplete structural parameters based on deep learning, which mainly comprises the following steps:
(1) The outside of the incomplete area of the statistical structural parameter information can acquire historical operation data, such as local historical wind speed, illumination, electricity price, temperature and gateway interaction power between the area and the power distribution network, and an equivalent model of the incomplete area of the structural parameter information is trained and established;
(2) Predicting probability distribution of meteorological data such as wind speed, illumination, temperature and the like and electricity price data before the day, substituting the probability distribution into an equivalent model of an area with incomplete structural parameter information, and calculating probability distribution of gateway interaction power between the area and a power distribution network;
(3) Constructing equivalent estimation points according to the predicted gateway interaction power probability distribution between the incomplete structure parameter information area and the power distribution network, and carrying out power distribution network probability load flow calculation;
(4) And (3) counting probability power flow calculation results of the power distribution network, analyzing probability distribution of state variables such as voltage amplitude, phase angle and the like of each node in the power distribution network, and evaluating overall operation risk of the power distribution network.
The method can realize the running risk assessment of the power distribution network under the condition of incomplete structural parameters, effectively avoid the problems that the traditional analysis method and the random sampling method need complete information to carry out probability tide calculation and risk assessment, be conductive to improving the running reliability of the power distribution network, improve the access level of distributed renewable energy sources, and have better application prospects.
The risk assessment flow of the invention is shown in fig. 1, and comprises the following steps:
1. and (3) carrying out statistics on the outside of the area with incomplete structural parameter information to obtain historical operation data such as local historical wind speed, illumination, electricity price, temperature and gateway interaction power between the area and the power distribution network, and training and establishing an equivalent model of the area with incomplete structural parameter information.
(1) The outside of the incomplete area of statistical analysis structural parameter information can acquire historical operation data, such as local historical illumination, wind speed, temperature, electricity price and gateway interaction power between the area and a power distribution network, and the data per unit, training set and test set division and other preprocessing is carried out on the historical operation data, as shown in formula (1):
Figure GDA0004231453980000091
in the formula ,Ds Historical data set representing illumination, wind speed, temperature, electricity price and gateway interaction power between incomplete structural parameter information area and power distribution network, wherein M is total number of days of historical data, and L k 、W k 、T k 、E k 、P g,k Respectively representing illumination, wind speed, temperature, electricity price and structural parameter information incomplete area on the kth day and a gateway interaction power data set between the distribution network,
Figure GDA0004231453980000101
respectively representing illumination, wind speed, temperature, electricity price, and gate interaction power between the incomplete structural parameter information area and the power distribution network at the kth and the d time period, wherein N represents the total time period number of a daily data set,'>
Figure GDA0004231453980000102
Representing the data set after per unit of the historical data set, min (·) representing the minimum value, and max (·) representing the maximum value,/->
Figure GDA0004231453980000103
Representing the training set taken from the per unit data set,/for>
Figure GDA0004231453980000104
Represents the test set taken from the per-unit data set and epsilon represents the proportion of the training set.
(2) Learning and training the training set data by adopting a long-short-term memory neural network (LSTM), and establishing an equivalent encapsulation model of the incomplete area of the structural parameter information, wherein the equivalent encapsulation model is shown in a formula (2):
Figure GDA0004231453980000105
in the formula ,xt Represents the t-th step of the current iteration from the training dataset
Figure GDA0004231453980000106
The data set of the illumination, wind speed, temperature and electricity price taken out from the device; h is a t-1 Representing +.>
Figure GDA0004231453980000107
The gateway interaction power set between the incomplete area of the extracted structural parameter information and the power distribution network is accumulated; f (f) t Representing forget gate output, w corresponding to the t step of the current iteration f and bf For the weight coefficient and bias coefficient of each neuron in the forgetting layer, sigma (·) represents an s-type curve function, i t Representing the output of the t-th input layer of the current iteration, w i and bi For weighting and bias coefficients of the neurons in the input layer, < >>
Figure GDA0004231453980000108
Representing estimated output of the convolution layer of the t step of the current iteration, w c and bc For the weighting and bias coefficients of each neuron in the convolution layer, tanh (·) represents the hyperbolic tangent function, c t Representative of the actual output of the current iteration step t convolution layer, o t Represents the output of the t-th output layer of the current iteration, w o and bo For the weight coefficient and bias coefficient of each neuron in the output layer, h t Representing the gateway interaction power between the incomplete structural parameter information area obtained by actual prediction of the t step of the current iteration and the power distribution network.
(3) Substituting the test set data to test and verify the equivalent packaging model, and optimally calculating and updating the weight coefficient and the bias coefficient of each layer of neurons of a long-short-time memory neural network (LSTM) according to the feedback result until the root mean square error converges:
1) Substituting test set data into an equivalent packaging model, and calculating a predicted value of the gateway interaction power between the incomplete area of the structural parameter information and the power distribution network:
Figure GDA0004231453980000111
in the formula ,
Figure GDA0004231453980000112
representing a predicted value of gate interaction power between the incomplete area of the structural parameter information and the power distribution network; x is x test Representing +.>
Figure GDA0004231453980000113
The data set of the illumination, wind speed, temperature and electricity price taken out from the device; f (F) grid (. Cndot.) refers to the equivalent encapsulation model of the incomplete area of the parameter information calculated in the step (1-2).
2) Comparing the predicted value and the actual value of the gate interaction power between the incomplete structure parameter information area and the power distribution network, and calculating the predicted root mean square error of the current packaging model, wherein the predicted root mean square error is shown in the following formula:
Figure GDA0004231453980000114
wherein, RMSE represents the prediction root mean square error of the current training encapsulation equivalent model; m is the number of the predicted total time period, t is the time period number,
Figure GDA0004231453980000115
representing +.>
Figure GDA0004231453980000116
The actual sampling value of the gate interaction power between the incomplete area of the structural parameter information taken out in the process and the power distribution network is +.>
Figure GDA0004231453980000117
Representing the predicted value of the gate interaction power between the incomplete area of the structural parameter information predicted by the formula (3) and the power distribution network.
3) And taking the statistical prediction root mean square error of the current encapsulation model as a target, taking the weight coefficient of each layer of neurons of the long short time memory neural network (LSTM) as an optimization decision variable, adopting a particle swarm algorithm to perform optimization calculation and adjusting the weight coefficient and the bias coefficient of each layer of neurons of the long short time memory neural network (LSTM) until the target converges. The following formula is shown:
Figure GDA0004231453980000118
Wherein, RMSE refers to root mean square error of power prediction by adopting an equivalent encapsulation model;
Figure GDA0004231453980000119
respectively taking the minimum and maximum values of the weight coefficients of the convolution layer; />
Figure GDA00042314539800001110
Respectively the minimum maximum value of the bias coefficients of the convolution layers;
Figure GDA00042314539800001111
Figure GDA00042314539800001112
respectively taking the minimum and maximum values of the weight coefficients of the input layer; />
Figure GDA00042314539800001113
Respectively taking the minimum and maximum values of the bias coefficients of the input layers; />
Figure GDA0004231453980000121
Respectively taking the minimum and maximum values of the weight coefficients of the forgetting layer; />
Figure GDA0004231453980000122
Respectively minimum and maximum values of the bias coefficients of the forgetting layers; />
Figure GDA0004231453980000123
Respectively taking the minimum and maximum values of the weight coefficients of the output layer;
Figure GDA0004231453980000124
respectively, the minimum and maximum values of the bias coefficients of the output layers.
2. Predicting probability distribution of meteorological data such as sunlight, wind speed and temperature and electricity price data before the day, substituting the probability distribution into an equivalent model of an area with incomplete structural parameter information, and calculating probability distribution of gateway interaction power between the area and a power distribution network.
(1) According to the probability distribution of weather data such as illumination, wind speed, temperature and the like and electricity price data predicted in the future, latin square sampling is adopted to generate a large number of simulation data samples, as shown in a formula (6):
Figure GDA0004231453980000125
wherein ,xpv 、x wind 、x TP 、x price Respectively representing the light, wind speed, temperature and electricity price data samples obtained by sampling the kth Latin square,
Figure GDA0004231453980000126
The probability distribution functions of illumination, wind speed, temperature and electricity price data predicted in the day before are respectively shown, N is the total sample rule number sampled by Latin square, and r n Representing random numbers between 0 and 1 subject to uniform distribution, k is the order number of the latin square samples.
(2) And (3) calling an equivalent model of the structural parameter information incomplete area obtained in the step (1), and simulating, calculating and predicting the gateway interaction power between the area and the power distribution network:
Figure GDA0004231453980000127
wherein ,xpv 、x wind 、x TP 、x price Respectively representing the light, wind speed, temperature and electricity price data samples obtained by sampling Latin square at the kth time, F grid (. Cndot.) refers to the equivalent encapsulation model of the incomplete area of the parameter information calculated in the step (1-2), x pre The data set is composed of illumination, wind speed, temperature and electricity price data samples obtained by sampling the kth Latin square;
Figure GDA0004231453980000128
representing a data set formed by the gateway interaction power between the structural parameter information incomplete area obtained by simulation calculation and the power distribution network.
(3) And (3) counting a gate interaction power data set between the predicted incomplete structure parameter information area and the power distribution network, and fitting probability distribution of the gate interaction power data set:
Figure GDA0004231453980000131
wherein ,
Figure GDA0004231453980000132
the 1 st, the 2 nd, the j th and the N th components in the gateway interaction power data set between the incomplete area of the predicted structural parameter information and the power distribution network are represented respectively; n is the dimension of a gateway interaction power data set between the predicted incomplete structure parameter information area and the power distribution network; mu, sigma and lambda are respectively the mean value, variance and skewness of the gateway interaction power data set between the predicted incomplete structure parameter information area and the power distribution network, E [. Cndot. ]To find the desired operator.
3. And constructing equivalent estimated points according to the predicted gateway interaction power probability distribution between the incomplete structure parameter information area and the power distribution network, and carrying out power distribution network probability load flow calculation.
(1) According to the statistical information of the predicted gateway interaction power probability distribution between the incomplete structure parameter information area and the power distribution network, constructing equivalent estimation points, as shown in a formula (9):
z k ＝μ+ξ k σ k＝1,2 (9)
wherein ,zk The method comprises the steps that k estimation points corresponding to a gateway interaction power data set between a structure parameter information incomplete area and a power distribution network are adopted, wherein the value of k is 1 or 2; zeta type toy k For a kth position measurement coefficient corresponding to a gateway interaction power data set between the structure parameter information incomplete area and the power distribution network, calculating the skewness lambda of the gateway interaction power data set between the structure parameter information incomplete area and the power distribution network through a formula (10):
Figure GDA0004231453980000133
wherein ,ξk K represents the number of the estimated point and takes 1 or 2 as the k-th position measurement coefficient corresponding to the gateway interaction power data set between the incomplete area of the structural parameter information and the power distribution network; lambda is the skewness of the gateway interaction power data set between the incomplete area of the structural parameter information and the power distribution network.
(2) And taking the equivalent estimated points of the gateway interaction power data set between the constructed structure parameter information incomplete area and the power distribution network as input to calculate the power flow of the power distribution network.
1) For equivalent estimated points of the gateway interaction power data set between the constructed structure parameter information incomplete area and the power distribution network, calculating weight coefficients of the estimated points in power flow calculation of the power distribution network through a formula (11):
Figure GDA0004231453980000141
wherein ,θk The method comprises the steps that a weight coefficient occupied by a kth estimated point corresponding to a gateway interaction power data set between a structural parameter information incomplete area and a power distribution network in power flow calculation is calculated, and pi is a calculated intermediate variableAnd the deviation lambda of the gateway interaction power data set between the incomplete area of the structural parameter information and the power distribution network is calculated, and k represents the number of the estimated point.
2) Estimating point z corresponding to gateway interaction power data set between imported structure parameter information incomplete area and power distribution network k Carrying out power flow calculation of the power distribution network; as shown in formula (12):
P j (k)＝f(z 1,k ,…,z i,k ,…,z M,k ,…,z M+1,k ,…,z 2M,k )k＝1,2 (12)
wherein ,Pj (k) The value of a j-th output state variable when the k-th estimated point of the power distribution network is input is obtained; f (·) is a power flow calculation equation of the power distribution network; m is the number of incomplete areas of the structural parameter information, and k represents the number of estimated points.
4. And (3) counting probability power flow calculation results of the power distribution network, analyzing probability distribution of output state variables such as voltage amplitude, phase angle and the like of each node in the power distribution network, and evaluating overall operation risk of the power distribution network.
(1) According to the probability power flow calculation result of the power distribution network, the probability distribution information of each moment of the output state variables such as the voltage amplitude, the phase angle and the like of each node of the power distribution network is statistically analyzed, and the probability distribution information is shown as a formula (13):
Figure GDA0004231453980000142
wherein ,Pj (k) And the value of the j-th output state variable when the k-th estimated point of the power distribution network is input is obtained. [ P ] j (k)] p Representative pair P j (k) To get the power of p, θ k The method comprises the steps that a weight coefficient occupied by a kth estimated point corresponding to a gateway interaction power data set between a structure parameter information incomplete area and a power distribution network in trend calculation is used, and M is the number of the structure parameter information incomplete areas;
Figure GDA0004231453980000143
substitution of j-th output state variable P in power grid j P-th order of (2), P is 1E (P j ) Represents the jthOutput state variable P j Is 2 +.>
Figure GDA0004231453980000144
Represents the j-th output state variable P j Second moment of>
Figure GDA0004231453980000145
For the j-th output state variable P in the distribution network j Is a variance of (c).
(2) Calculating out-of-limit values and out-of-limit severity of output state variables such as voltage of each node and branch current in a power distribution network, wherein the out-of-limit values and the out-of-limit severity are shown in the following formula:
Figure GDA0004231453980000146
Figure GDA0004231453980000151
Figure GDA0004231453980000152
Wherein i is the number of a node in the power distribution network, and j is the number of a branch in the power distribution network; v (V) out,i The more limited the voltage at node I is, I out,j U is the current of branch j is the more limited value i 、U i,min 、U i,max The actual voltage value, the minimum allowable voltage amplitude and the maximum allowable voltage amplitude of the node i are respectively; i j For the actual operating current, I, of branch j j,max Maximum allowable current amplitude for branch j; s is S ev (V out,i ) For the voltage out-of-limit severity of the ith node, S ev (I out,j ) For the current out-of-limit severity of the jth branch, A i 、B i 、C i Fitting parameters, alpha, of voltage out-of-limit severity functions of ith node respectively j 、β j 、δ j Fitting parameters for the current out-of-limit severity functions of the jth branch, exp (·) representing the value of the natural constante is an exponential function of the base, out represents the Out-of-limit value of the voltage or current.
(3) Calculating and evaluating the overall operation risk of the power distribution network according to the threshold value, the threshold severity and the threshold probability of output state variables such as voltage of each node and branch current in the power distribution network, wherein the overall operation risk is shown in the following formula:
Figure GDA0004231453980000153
wherein R is a total running risk value of the system, i is the number of nodes in the power distribution network, D is the total number of nodes in the power distribution network, j is the number of branches in the power distribution network, and L is the total number of branches in the power distribution network.
Figure GDA0004231453980000154
For the voltage cumulative distribution function of node i, +. >
Figure GDA0004231453980000155
For the current cumulative distribution function of branch j, S ev (V out,i ) For the voltage out-of-limit severity of node i, S ev (I out,j ) The current out-of-limit severity for branch j.
Figure GDA0004231453980000156
The probability density function of the corresponding node voltage can be calculated according to the probability distribution information of the voltage state variables of each node in the formula (13), and then the probability density function is obtained by integrating and solving. />
Figure GDA0004231453980000157
The probability density function of the corresponding branch current can be calculated according to the probability distribution information of the state variables of the branch current in the formula (13), and then the probability density function is integrated and solved. />

Claims (1)

1. The risk assessment method for the power distribution network under the incomplete structural parameters based on the deep learning is characterized by comprising the following steps of:
(1) The outside of the incomplete area of statistical structural parameter information can acquire historical operation data: the method comprises the steps of training and establishing an equivalent model of a region with incomplete structural parameter information by local historical wind speed, illumination, electricity price, temperature and gateway interaction power between the region and a power distribution network;
(2) Predicting probability distribution of wind speed, illumination, temperature and electricity price data before the day, substituting an equivalent model of an incomplete area of structural parameter information, and calculating probability distribution of gateway interaction power between the area and a power distribution network;
(3) Constructing equivalent estimation points according to the predicted gateway interaction power probability distribution between the incomplete structure parameter information area and the power distribution network, and carrying out power distribution network probability load flow calculation;
(4) Calculating a probability power flow calculation result of the power distribution network, analyzing probability distribution of voltage amplitude and phase angle state variables of each node in the power distribution network, and evaluating overall operation risk of the power distribution network;
in the step (1), historical operation data can be acquired outside the incomplete structure parameter information area, and the steps of training and establishing an equivalent model of the incomplete structure parameter information area are as follows:
step (1-1): the outside of the incomplete area of statistical analysis structural parameter information can acquire historical operation data, local historical illumination, wind speed, temperature, electricity price and gateway interaction power between the area and a power distribution network, and the data per unit, training set and test set division preprocessing is carried out on the historical operation data, as shown in formula (1):
Figure FDA0004231453970000011
in the formula ,Ds Historical data set representing illumination, wind speed, temperature, electricity price and gateway interaction power between incomplete structural parameter information area and power distribution network, wherein M is total number of days of historical data, and L k 、W k 、T k 、E k 、P g,k Respectively representing illumination, wind speed, temperature, electricity price and structural parameter information incomplete area on the kth day and a gateway interaction power data set between the distribution network,
Figure FDA0004231453970000021
respectively representing illumination, wind speed, temperature, electricity price, and gate interaction power between the incomplete structural parameter information area and the power distribution network at the kth and the d time period, wherein N represents the total time period number of a daily data set,'>
Figure FDA0004231453970000022
Representing the data set after per unit of the historical data set, min (·) representing the minimum value, and max (·) representing the maximum value,/->
Figure FDA0004231453970000023
Representing the training set taken from the per unit data set,/for>
Figure FDA0004231453970000024
Represents the test set taken out from the data set after per unit, epsilon represents the proportion of the training set;
step (1-2): learning and training the training set data by adopting a long-short-term memory neural network LSTM, and establishing an equivalent packaging model of the incomplete area of the structural parameter information, wherein the equivalent packaging model is shown in a formula (2):
Figure FDA0004231453970000025
in the formula ,xt Represents the t-th step of the current iteration from the training dataset
Figure FDA0004231453970000026
The data set of the illumination, wind speed, temperature and electricity price taken out from the device; h is a t-1 Representing the slave training prior to the t-th step of the current iterationData set->
Figure FDA0004231453970000027
The gateway interaction power set between the incomplete area of the extracted structural parameter information and the power distribution network is accumulated; f (f) t Representing forget gate output, w corresponding to the t step of the current iteration f and bf For the weight coefficient and bias coefficient of each neuron in the forgetting layer, sigma (·) represents an s-type curve function, i t Representing the output of the t-th input layer of the current iteration, w i and bi For weighting and bias coefficients of the neurons in the input layer, < >>
Figure FDA0004231453970000028
Representing estimated output of the convolution layer of the t step of the current iteration, w c and bc For the weighting and bias coefficients of each neuron in the convolution layer, tanh (·) represents the hyperbolic tangent function, c t Representative of the actual output of the current iteration step t convolution layer, o t Represents the output of the t-th output layer of the current iteration, w o and bo For the weight coefficient and bias coefficient of each neuron in the output layer, h t Representing the gateway interaction power between the incomplete structural parameter information area obtained by actual prediction of the t step of the current iteration and the power distribution network;
step (1-3): substituting the test set data, performing test verification on the equivalent encapsulation model, and optimally calculating and updating the weight coefficient and the bias coefficient of each layer of neurons of the long-short-time memory neural network LSTM according to the feedback result until the root mean square error converges:
1) Substituting test set data into an equivalent packaging model, and calculating a predicted value of the gateway interaction power between the incomplete area of the structural parameter information and the power distribution network:
Figure FDA0004231453970000031
in the formula ,
Figure FDA0004231453970000032
representing a predicted value of gate interaction power between the incomplete area of the structural parameter information and the power distribution network; x is x test Representing +.>
Figure FDA0004231453970000033
The data set of the illumination, wind speed, temperature and electricity price taken out from the device; f (F) grid (. Cndot.) refers to the equivalent encapsulation model of the incomplete area of parameter information calculated in the step (1-2);
2) Comparing the predicted value and the actual value of the gate interaction power between the incomplete structure parameter information area and the power distribution network, and calculating the predicted root mean square error of the current packaging model, wherein the predicted root mean square error is shown in the following formula:
Figure FDA0004231453970000034
wherein, RMSE represents the prediction root mean square error of the current training encapsulation equivalent model; m is the number of the predicted total time period, t is the time period number,
Figure FDA0004231453970000035
representing +.>
Figure FDA0004231453970000036
The actual sampling value of the gate interaction power between the incomplete area of the structural parameter information taken out in the process and the power distribution network is +.>
Figure FDA0004231453970000037
Representing a gate interaction power predicted value between the incomplete structure parameter information area predicted by the formula (3) and the power distribution network;
3) Taking the statistical prediction root mean square error of the current encapsulation model as a target, taking the weight coefficient of each layer of neurons of the long-short-term memory neural network LSTM as an optimization decision variable, adopting a particle swarm algorithm to perform optimization calculation and adjusting the weight coefficient and the bias coefficient of each layer of neurons of the long-short-term memory neural network LSTM until the target converges, wherein the weight coefficient and the bias coefficient are as shown in the following formula:
Figure FDA0004231453970000038
Wherein, RMSE refers to root mean square error of power prediction by adopting an equivalent encapsulation model;
Figure FDA0004231453970000039
respectively taking the minimum and maximum values of the weight coefficients of the convolution layer; />
Figure FDA00042314539700000310
Respectively the minimum maximum value of the bias coefficients of the convolution layers; />
Figure FDA00042314539700000311
Figure FDA00042314539700000312
Respectively taking the minimum and maximum values of the weight coefficients of the input layer; />
Figure FDA00042314539700000313
Respectively taking the minimum and maximum values of the bias coefficients of the input layers; />
Figure FDA00042314539700000314
Respectively taking the minimum and maximum values of the weight coefficients of the forgetting layer; />
Figure FDA00042314539700000315
Respectively minimum and maximum values of the bias coefficients of the forgetting layers; />
Figure FDA00042314539700000316
Respectively taking the minimum and maximum values of the weight coefficients of the output layer;
Figure FDA00042314539700000317
respectively taking the minimum and maximum values of the bias coefficients of the output layers;
in the step (2), predicting probability distribution of light, wind speed, temperature and electricity price data before the day, substituting the probability distribution into an equivalent model of an area with incomplete structural parameter information, and calculating probability distribution of gateway interaction power between the area and a power distribution network, wherein the probability distribution is specifically as follows:
step (2-1): according to the probability distribution of the illumination, wind speed, temperature and electricity price data predicted in the day, latin square sampling is adopted to generate a large number of simulation data samples, as shown in a formula (6):
Figure FDA0004231453970000041
wherein ,xpv 、x wind 、x TP 、x price Respectively representing the light, wind speed, temperature and electricity price data samples obtained by sampling the kth Latin square,
Figure FDA0004231453970000042
The probability distribution functions of illumination, wind speed, temperature and electricity price data predicted in the day before are respectively shown, N is the total sample rule number sampled by Latin square, and r n Representing random numbers between 0 and 1 subject to uniform distribution, k being the order number of Latin square samples;
step (2-2): and (3) calling an equivalent model of the structural parameter information incomplete area obtained in the step (1), and simulating, calculating and predicting the gateway interaction power between the area and the power distribution network:
Figure FDA0004231453970000043
wherein ,xpv 、x wind 、x TP 、x price Respectively representing the light, wind speed, temperature and electricity price data samples obtained by sampling Latin square at the kth time, F grid (·)Refer to the equivalent encapsulation model of the incomplete area of the parameter information calculated in the step (1-2), x pre The data set is composed of illumination, wind speed, temperature and electricity price data samples obtained by sampling the kth Latin square;
Figure FDA0004231453970000044
representing a data set formed by the gateway interaction power between the incomplete structural parameter information area obtained by simulation calculation and the power distribution network;
step (2-3): and (3) counting a gate interaction power data set between the predicted incomplete structure parameter information area and the power distribution network, and fitting probability distribution of the gate interaction power data set:
Figure FDA0004231453970000045
wherein ,
Figure FDA0004231453970000051
the 1 st, the 2 nd, the j th and the N th components in the gateway interaction power data set between the incomplete area of the predicted structural parameter information and the power distribution network are represented respectively; n is the dimension of a gateway interaction power data set between the predicted incomplete structure parameter information area and the power distribution network; mu, sigma and lambda are respectively the mean value, variance and skewness of the gateway interaction power data set between the predicted incomplete structure parameter information area and the power distribution network, E [. Cndot. ]To calculate the expected operator;
in the step (3), according to the predicted probability distribution of the gateway interaction power between the incomplete structure parameter information area and the power distribution network, constructing equivalent estimation points, and performing power distribution network probability load flow calculation, specifically as follows:
step (3-1): according to the statistical information of the predicted gateway interaction power probability distribution between the incomplete structure parameter information area and the power distribution network, constructing equivalent estimation points, as shown in a formula (9):
z k ＝μ+ξ k σ k＝1,2 (9)
wherein ,zk The method comprises the steps that k estimation points corresponding to a gateway interaction power data set between a structure parameter information incomplete area and a power distribution network are adopted, wherein the value of k is 1 or 2; zeta type toy k For a kth position measurement coefficient corresponding to a gateway interaction power data set between the structure parameter information incomplete area and the power distribution network, calculating the skewness lambda of the gateway interaction power data set between the structure parameter information incomplete area and the power distribution network through a formula (10):
Figure FDA0004231453970000052
wherein ,ξk K represents the number of the estimated point and takes 1 or 2 as the k-th position measurement coefficient corresponding to the gateway interaction power data set between the incomplete area of the structural parameter information and the power distribution network; lambda is the skewness of a gateway interaction power data set between the incomplete area of the structural parameter information and the power distribution network;
Step (3-2): taking the equivalent estimated points of the gateway interaction power data set between the constructed structure parameter information incomplete area and the power distribution network as input, and carrying out power flow calculation of the power distribution network;
1) For equivalent estimated points of the gateway interaction power data set between the constructed structure parameter information incomplete area and the power distribution network, calculating weight coefficients of the estimated points in power flow calculation of the power distribution network through a formula (11):
Figure FDA0004231453970000053
wherein ,θk The method comprises the steps that a weight coefficient occupied by a kth estimated point corresponding to a gateway interaction power data set between a structure parameter information incomplete area and a power distribution network in power flow calculation is calculated, pi is a calculated intermediate variable, the weight coefficient is calculated by the skewness lambda of the gateway interaction power data set between the structure parameter information incomplete area and the power distribution network, and k represents an estimated point number;
2) Importing structural parametersEstimating point z corresponding to gateway interaction power data set between incomplete information area and power distribution network k Carrying out power flow calculation of the power distribution network; as shown in formula (12):
P j (k)＝f(z 1,k ,…,z i,k ,…,z M,k ,…,z M+1,k ,…,z 2M,k ) k＝1,2 (12)
wherein ,Pj (k) The value of a j-th output state variable when the k-th estimated point of the power distribution network is input is obtained; f (·) is a power flow calculation equation of the power distribution network; m is the number of incomplete areas of the structural parameter information, and k represents the number of estimated points;
In the step (4), a power distribution network probability power flow calculation result is counted, probability distribution of voltage amplitude and phase angle output state variables of each node in the power distribution network is analyzed, and overall operation risk of the power distribution network is estimated, wherein the method specifically comprises the following steps:
step (4-1): according to the probability power flow calculation result of the power distribution network, the probability distribution information of each moment of the voltage amplitude and the phase angle output state variable of each node of the power distribution network is statistically analyzed, and the probability distribution information is shown as a formula (13):
Figure FDA0004231453970000061
wherein ,Pj (k) The value of a j-th output state variable when the k-th estimated point of the power distribution network is input is obtained; [ P ] j (k)] p Representative pair P j (k) To get the power of p, θ k The method comprises the steps that a weight coefficient occupied by a kth estimated point corresponding to a gateway interaction power data set between a structure parameter information incomplete area and a power distribution network in trend calculation is used, and M is the number of the structure parameter information incomplete areas;
Figure FDA0004231453970000062
substitution of j-th output state variable P in power grid j P-th order of (2), P is 1E (P j ) Represents the j-th output state variable P j Is 2 +.>
Figure FDA0004231453970000063
Represents the j-th output state variable P j Second moment of>
Figure FDA0004231453970000064
For the j-th output state variable P in the distribution network j Is a variance of (2);
step (4-2): calculating the threshold value and the threshold severity of each node voltage and branch current output state variable in the power distribution network, wherein the threshold value and the threshold severity are as follows:
Figure FDA0004231453970000065
Figure FDA0004231453970000066
Figure FDA0004231453970000067
Wherein i is the number of a node in the power distribution network, and j is the number of a branch in the power distribution network; v (V) out,i The more limited the voltage at node I is, I out,j U is the current of branch j is the more limited value i 、U i,min 、U i,max The actual voltage value, the minimum allowable voltage amplitude and the maximum allowable voltage amplitude of the node i are respectively; i j For the actual operating current, I, of branch j j,max Maximum allowable current amplitude for branch j; s is S ev (V out,i ) For the voltage out-of-limit severity of the ith node, S ev (I out,j ) For the current out-of-limit severity of the jth branch, A i 、B i 、C i Fitting parameters, alpha, of voltage out-of-limit severity functions of ith node respectively j 、β j 、δ j Fitting parameters for the current Out-of-limit severity function of the jth branch, exp (·) representing an exponential function based on a natural constant e, out representing voltage or electricity, respectivelyAn out-of-limit value for the stream;
step (4-3): calculating and evaluating the overall operation risk of the power distribution network according to the threshold value, the threshold severity and the threshold probability of the output state variables of the voltage and the branch current of each node in the power distribution network, wherein the overall operation risk is shown in the following formula:
Figure FDA0004231453970000071
wherein R is the total running risk value of the system, i is the number of nodes in the power distribution network, D is the total number of nodes in the power distribution network, j is the number of branches in the power distribution network, L is the total number of branches in the power distribution network,
Figure FDA0004231453970000072
for the voltage cumulative distribution function of node i, +. >
Figure FDA0004231453970000073
For the current cumulative distribution function of branch j, S ev (V out,i ) For the voltage out-of-limit severity of node i, S ev (I out,j ) The current out-of-limit severity for branch j;
Figure FDA0004231453970000074
the probability distribution information of the voltage state variables of each node in the formula (13) can be used for calculating the probability density function of the corresponding node voltage, and then the probability density function is integrated and solved to obtain +.>
Figure FDA0004231453970000075
The probability density function of the corresponding branch current can be calculated according to the probability distribution information of the state variables of the branch current in the formula (13), and then the probability density function is integrated and solved.
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